Electron. J. Diff. Equ., Vol. 2011 (2011), No. 84, pp. 1-10.

Fundamental solutions to the p-Laplace equation in a class of Grushin vector fields

Thomas Bieske

We find the fundamental solution to the p-Laplace equation in a class of Grushin-type spaces. The singularity occurs at the sub-Riemannian points, which naturally corresponds to finding the fundamental solution of a generalized Grushin operator in Euclidean space. We then use this solution to find an infinite harmonic function with specific boundary data and to compute the capacity of annuli centered at the singularity.

Submitted December 10, 2010. Published June 29, 2011.
Math Subject Classifications: 35H20, 53C17, 17B70
Key Words: Grushin-type spaces; p-Laplacian.

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Thomas Bieske
Department of Mathematics
University of South Florida
Tampa, FL 33620, USA
email: tbieske@math.usf.edu

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